%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP013_3 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:35:36 AM UTC 2026
% Result : Theorem 23.69s 8.74s
% Output : Refutation 23.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 47
% Syntax : Number of formulae : 184 ( 89 unt; 0 typ; 2 def)
% Number of atoms : 673 ( 198 equ; 0 cnn)
% Maximal formula atoms : 25 ( 3 avg)
% Number of connectives : 2339 ( 143 ~; 68 |; 77 &;1915 @)
% ( 25 <=>; 111 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 41 usr; 15 con; 0-4 aty)
% Number of variables : 337 ( 0 ^; 332 !; 3 ?; 337 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Enum_2Enum_type,type,
tyop_2Enum_2Enum: $tType ).
thf(skt1_type,type,
skt1: $tType ).
thf(app_2E2_decl,type,
app_2E2:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ tyop_2Emin_2Efun ) ) > TB > TA ) ).
thf(p_decl,type,
p: tyop_2Emin_2Ebool > $o ).
thf(combin_i_2E0_decl,type,
combin_i_2E0:
!>[TA: $tType] : ( TA @ ( TA @ tyop_2Emin_2Efun ) ) ).
thf(combin_k_2E0_decl,type,
combin_k_2E0:
!>[TA: $tType,TB: $tType] : ( TB @ ( TA @ tyop_2Emin_2Efun ) @ ( TB @ tyop_2Emin_2Efun ) ) ).
thf(combin_s_2E0_decl,type,
combin_s_2E0:
!>[TA: $tType,TB: $tType,TC: $tType] : ( TA @ ( TC @ tyop_2Emin_2Efun ) @ ( TB @ ( TC @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) @ ( TA @ ( TB @ tyop_2Emin_2Efun ) @ ( TC @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ).
thf(c_2Ebool_2E_21_2E0_decl,type,
c_2Ebool_2E_21_2E0:
!>[TA: $tType] : ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ).
thf(c_2Ebool_2E_21_2E1_decl,type,
c_2Ebool_2E_21_2E1:
!>[TA: $tType] : ( ( tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun ) ) > tyop_2Emin_2Ebool ) ).
thf(c_2Earithmetic_2E_2B_2E0_decl,type,
c_2Earithmetic_2E_2B_2E0: tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) ).
thf(c_2Earithmetic_2E_2B_2E2_decl,type,
c_2Earithmetic_2E_2B_2E2: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2E_2D_2E0_decl,type,
c_2Earithmetic_2E_2D_2E0: tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) ).
thf(c_2Earithmetic_2E_2D_2E2_decl,type,
c_2Earithmetic_2E_2D_2E2: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebool_2E_2F_5C_2E0_decl,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) ).
thf(c_2Ebool_2E_2F_5C_2E2_decl,type,
c_2Ebool_2E_2F_5C_2E2: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
thf(c_2Earithmetic_2E_3C_3D_2E0_decl,type,
c_2Earithmetic_2E_3C_3D_2E0: tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) ).
thf(c_2Earithmetic_2E_3C_3D_2E2_decl,type,
c_2Earithmetic_2E_3C_3D_2E2: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Emin_2Ebool ).
thf(c_2Emin_2E_3D_2E0_decl,type,
c_2Emin_2E_3D_2E0:
!>[TA: $tType] : ( tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun ) @ ( TA @ tyop_2Emin_2Efun ) ) ).
thf(c_2Emin_2E_3D_2E2_decl,type,
c_2Emin_2E_3D_2E2:
!>[TA: $tType] : ( TA > TA > tyop_2Emin_2Ebool ) ).
thf(c_2Emin_2E_3D_3D_3E_2E0_decl,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) ).
thf(c_2Emin_2E_3D_3D_3E_2E2_decl,type,
c_2Emin_2E_3D_3D_3E_2E2: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
thf(c_2Ebool_2E_3F_2E0_decl,type,
c_2Ebool_2E_3F_2E0:
!>[TA: $tType] : ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ).
thf(c_2Ebool_2E_3F_2E1_decl,type,
c_2Ebool_2E_3F_2E1:
!>[TA: $tType] : ( ( tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun ) ) > tyop_2Emin_2Ebool ) ).
thf(c_2Ebool_2ECOND_2E0_decl,type,
c_2Ebool_2ECOND_2E0:
!>[TA: $tType] : ( TA @ ( TA @ tyop_2Emin_2Efun ) @ ( TA @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) ) ).
thf(c_2Ebool_2ECOND_2E3_decl,type,
c_2Ebool_2ECOND_2E3:
!>[TA: $tType] : ( tyop_2Emin_2Ebool > TA > TA > TA ) ).
thf(c_2Ebool_2EF_2E0_decl,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
thf(c_2Ebool_2ET_2E0_decl,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
thf(c_2Ebool_2E_5C_2F_2E0_decl,type,
c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) ).
thf(c_2Ebool_2E_5C_2F_2E2_decl,type,
c_2Ebool_2E_5C_2F_2E2: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
thf(c_2Ewords_2En2w_2E0_decl,type,
c_2Ewords_2En2w_2E0:
!>[TA: $tType] : ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) ) ).
thf(c_2Ewords_2En2w_2E1_decl,type,
c_2Ewords_2En2w_2E1:
!>[TA: $tType] : ( tyop_2Enum_2Enum > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) ) ).
thf(c_2Ewords_2Eword__2comp_2E0_decl,type,
c_2Ewords_2Eword__2comp_2E0:
!>[TA: $tType] : ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) ) ).
thf(c_2Ewords_2Eword__2comp_2E1_decl,type,
c_2Ewords_2Eword__2comp_2E1:
!>[TA: $tType] : ( ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) ) ).
thf(c_2Ewords_2Eword__add_2E0_decl,type,
c_2Ewords_2Eword__add_2E0:
!>[TA: $tType] : ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) ) ).
thf(c_2Ewords_2Eword__add_2E2_decl,type,
c_2Ewords_2Eword__add_2E2:
!>[TA: $tType] : ( ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) ) ).
thf(c_2Ewords_2Eword__sub_2E0_decl,type,
c_2Ewords_2Eword__sub_2E0:
!>[TA: $tType] : ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) ) ).
thf(c_2Ewords_2Eword__sub_2E2_decl,type,
c_2Ewords_2Eword__sub_2E2:
!>[TA: $tType] : ( ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) ) ).
thf(c_2Ebool_2E_7E_2E0_decl,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) ).
thf(c_2Ebool_2E_7E_2E1_decl,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
thf(sk1_decl,type,
sk1: tyop_2Enum_2Enum ).
thf(sk2_decl,type,
sk2: tyop_2Enum_2Enum ).
thf(sk1_def,definition,
( sk1
= ( @+[A: tyop_2Enum_2Enum] :
~ ! [B: tyop_2Enum_2Enum] :
( ( A @ ( B @ c_2Earithmetic_2E_3C_3D_2E2 ) @ p )
=> ( ( B @ ( A @ c_2Earithmetic_2E_2D_2E2 ) @ ( skt1 @ c_2Ewords_2En2w_2E1 ) )
= ( B @ ( skt1 @ c_2Ewords_2En2w_2E1 ) @ ( A @ ( skt1 @ c_2Ewords_2En2w_2E1 ) @ ( skt1 @ c_2Ewords_2Eword__sub_2E2 ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: tyop_2Enum_2Enum] :
~ ( ( sk1 @ ( A @ c_2Earithmetic_2E_3C_3D_2E2 ) @ p )
=> ( ( A @ ( sk1 @ c_2Earithmetic_2E_2D_2E2 ) @ ( skt1 @ c_2Ewords_2En2w_2E1 ) )
= ( A @ ( skt1 @ c_2Ewords_2En2w_2E1 ) @ ( sk1 @ ( skt1 @ c_2Ewords_2En2w_2E1 ) @ ( skt1 @ c_2Ewords_2Eword__sub_2E2 ) ) ) ) ) ) ) ).
thf(27,axiom,
! [A: tyop_2Emin_2Ebool] :
( ( ( A = c_2Ebool_2EF_2E0 )
<=> ~ ( A @ p ) )
& ( ( c_2Ebool_2EF_2E0 = A )
<=> ~ ( A @ p ) )
& ( ( A = c_2Ebool_2ET_2E0 )
<=> ( A @ p ) )
& ( ( c_2Ebool_2ET_2E0 = A )
<=> ( A @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
thf(159,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ~ ( A @ p )
=> ( A = c_2Ebool_2EF_2E0 ) )
& ( ( A = c_2Ebool_2EF_2E0 )
=> ~ ( A @ p ) )
& ( ~ ( A @ p )
=> ( c_2Ebool_2EF_2E0 = A ) )
& ( ( c_2Ebool_2EF_2E0 = A )
=> ~ ( A @ p ) )
& ( ( A @ p )
=> ( A = c_2Ebool_2ET_2E0 ) )
& ( ( A = c_2Ebool_2ET_2E0 )
=> ( A @ p ) )
& ( ( A @ p )
=> ( c_2Ebool_2ET_2E0 = A ) )
& ( ( c_2Ebool_2ET_2E0 = A )
=> ( A @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(160,plain,
( ! [A: tyop_2Emin_2Ebool] :
( ~ ( A @ p )
=> ( A = c_2Ebool_2EF_2E0 ) )
& ! [A: tyop_2Emin_2Ebool] :
( ( A = c_2Ebool_2EF_2E0 )
=> ~ ( A @ p ) )
& ! [A: tyop_2Emin_2Ebool] :
( ~ ( A @ p )
=> ( c_2Ebool_2EF_2E0 = A ) )
& ! [A: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2EF_2E0 = A )
=> ~ ( A @ p ) )
& ! [A: tyop_2Emin_2Ebool] :
( ( A @ p )
=> ( A = c_2Ebool_2ET_2E0 ) )
& ! [A: tyop_2Emin_2Ebool] :
( ( A = c_2Ebool_2ET_2E0 )
=> ( A @ p ) )
& ! [A: tyop_2Emin_2Ebool] :
( ( A @ p )
=> ( c_2Ebool_2ET_2E0 = A ) )
& ! [A: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2ET_2E0 = A )
=> ( A @ p ) ) ),
inference(miniscope,[status(thm)],[159]) ).
thf(161,plain,
! [H: tyop_2Emin_2Ebool,G: tyop_2Emin_2Ebool,F: tyop_2Emin_2Ebool,E: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,A: tyop_2Emin_2Ebool] :
( ( ( H = c_2Ebool_2EF_2E0 )
| ( H @ p ) )
& ( ~ ( G @ p )
| ( G != c_2Ebool_2EF_2E0 ) )
& ( ( c_2Ebool_2EF_2E0 = F )
| ( F @ p ) )
& ( ~ ( E @ p )
| ( c_2Ebool_2EF_2E0 != E ) )
& ( ( D = c_2Ebool_2ET_2E0 )
| ~ ( D @ p ) )
& ( ( C @ p )
| ( C != c_2Ebool_2ET_2E0 ) )
& ( ( c_2Ebool_2ET_2E0 = B )
| ~ ( B @ p ) )
& ( ( A @ p )
| ( c_2Ebool_2ET_2E0 != A ) ) ),
inference(cnf,[status(esa)],[160]) ).
thf(169,plain,
! [A: tyop_2Emin_2Ebool] :
( ( A @ p )
| ( A != c_2Ebool_2ET_2E0 ) ),
inference(cnfConj,[status(thm)],[161]) ).
thf(174,plain,
! [A: tyop_2Emin_2Ebool] :
( ( A @ p )
| ( A != c_2Ebool_2ET_2E0 ) ),
inference(lifteq,[status(thm)],[169]) ).
thf(175,plain,
c_2Ebool_2ET_2E0 @ p,
inference(simp,[status(thm)],[174]) ).
thf(1,conjecture,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( A @ ( B @ c_2Earithmetic_2E_3C_3D_2E2 ) @ p )
=> ( ( B @ ( A @ c_2Earithmetic_2E_2D_2E2 ) @ ( TA @ c_2Ewords_2En2w_2E1 ) )
= ( B @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( A @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2En2w__sub) ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( A @ ( B @ c_2Earithmetic_2E_3C_3D_2E2 ) @ p )
=> ( ( B @ ( A @ c_2Earithmetic_2E_2D_2E2 ) @ ( TA @ c_2Ewords_2En2w_2E1 ) )
= ( B @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( A @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(47,plain,
~ ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( A @ ( B @ c_2Earithmetic_2E_3C_3D_2E2 ) @ p )
=> ( ( B @ ( A @ c_2Earithmetic_2E_2D_2E2 ) @ ( TA @ c_2Ewords_2En2w_2E1 ) )
= ( B @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( A @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(48,plain,
( ( ( sk2 @ ( sk1 @ c_2Earithmetic_2E_2D_2E2 ) @ ( skt1 @ c_2Ewords_2En2w_2E1 ) )
!= ( sk2 @ ( skt1 @ c_2Ewords_2En2w_2E1 ) @ ( sk1 @ ( skt1 @ c_2Ewords_2En2w_2E1 ) @ ( skt1 @ c_2Ewords_2Eword__sub_2E2 ) ) ) )
& ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ p ) ),
inference(cnf,[status(esa)],[47]) ).
thf(49,plain,
sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ p,
inference(cnfConj,[status(thm)],[48]) ).
thf(21,axiom,
! [A: tyop_2Emin_2Ebool] :
( ~ ( A @ p )
<=> ( A @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_7E_2E1) ).
thf(117,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ( A @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p )
=> ~ ( A @ p ) )
& ( ~ ( A @ p )
=> ( A @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(118,plain,
( ! [A: tyop_2Emin_2Ebool] :
( ( A @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p )
=> ~ ( A @ p ) )
& ! [A: tyop_2Emin_2Ebool] :
( ~ ( A @ p )
=> ( A @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ) ),
inference(miniscope,[status(thm)],[117]) ).
thf(119,plain,
! [B: tyop_2Emin_2Ebool,A: tyop_2Emin_2Ebool] :
( ( ~ ( B @ p )
| ~ ( B @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) )
& ( ( A @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p )
| ( A @ p ) ) ),
inference(cnf,[status(esa)],[118]) ).
thf(121,plain,
! [A: tyop_2Emin_2Ebool] :
( ~ ( A @ p )
| ~ ( A @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ),
inference(cnfConj,[status(thm)],[119]) ).
thf(122,plain,
! [A: tyop_2Emin_2Ebool] :
( ~ ( A @ p )
| ~ ( A @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ),
inference(simp,[status(thm)],[121]) ).
thf(361,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ p )
!= ( A @ p ) )
| ~ $true
| ~ ( A @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ),
inference(paramod_ordered,[status(thm)],[49,122]) ).
thf(362,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ p )
!= ( A @ p ) )
| ~ ( A @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ),
inference(simp,[status(thm)],[361]) ).
thf(363,plain,
~ ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ),
inference(pattern_uni,[status(thm)],[362:[bind(A,$thf( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) ))]]) ).
thf(380,plain,
( ( ( c_2Ebool_2ET_2E0 @ p )
!= ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[175,363]) ).
thf(381,plain,
( ( c_2Ebool_2ET_2E0 @ p )
!= ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ),
inference(simp,[status(thm)],[380]) ).
thf(384,plain,
( c_2Ebool_2ET_2E0
!= ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) ) ),
inference(simp,[status(thm)],[381]) ).
thf(10,axiom,
! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
= ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27a) ).
thf(77,plain,
! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
= ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(18,axiom,
~ ( c_2Ebool_2EF_2E0 @ p ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Enotfalse) ).
thf(101,plain,
~ ( c_2Ebool_2EF_2E0 @ p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(102,plain,
~ ( c_2Ebool_2EF_2E0 @ p ),
inference(polarity_switch,[status(thm)],[101]) ).
thf(309,plain,
( ( ( c_2Ebool_2ET_2E0 @ p )
!= ( c_2Ebool_2EF_2E0 @ p ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[175,102]) ).
thf(310,plain,
( ( c_2Ebool_2ET_2E0 @ p )
!= ( c_2Ebool_2EF_2E0 @ p ) ),
inference(simp,[status(thm)],[309]) ).
thf(311,plain,
c_2Ebool_2ET_2E0 != c_2Ebool_2EF_2E0,
inference(simp,[status(thm)],[310]) ).
thf(8,axiom,
! [TA: $tType] :
( ! [A: TA,B: TA] :
( ( B @ ( A @ ( c_2Ebool_2EF_2E0 @ ( TA @ c_2Ebool_2ECOND_2E3 ) ) ) )
= B )
& ! [A: TA,B: TA] :
( ( B @ ( A @ ( c_2Ebool_2ET_2E0 @ ( TA @ c_2Ebool_2ECOND_2E3 ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__case__thm) ).
thf(67,plain,
! [TA: $tType] :
( ! [A: TA,B: TA] :
( ( B @ ( A @ ( c_2Ebool_2EF_2E0 @ ( TA @ c_2Ebool_2ECOND_2E3 ) ) ) )
= B )
& ! [A: TA,B: TA] :
( ( B @ ( A @ ( c_2Ebool_2ET_2E0 @ ( TA @ c_2Ebool_2ECOND_2E3 ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(24,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( B @ ( A @ c_2Emin_2E_3D_3D_3E_2E2 ) @ p )
<=> ( ( A @ p )
=> ( B @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_3D_3D_3E) ).
thf(138,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( A @ p )
=> ( B @ p ) )
=> ( B @ ( A @ c_2Emin_2E_3D_3D_3E_2E2 ) @ p ) )
& ( ( B @ ( A @ c_2Emin_2E_3D_3D_3E_2E2 ) @ p )
=> ( ( A @ p )
=> ( B @ p ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(3,axiom,
! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
= ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ewords_2Eword__add_2E2_2Emono_2EA_27b) ).
thf(52,plain,
! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
= ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(20,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( B @ ( A @ ( TA @ c_2Emin_2E_3D_2E2 ) ) @ p )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_3D) ).
thf(110,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( A = B )
=> ( B @ ( A @ ( TA @ c_2Emin_2E_3D_2E2 ) ) @ p ) )
& ( ( B @ ( A @ ( TA @ c_2Emin_2E_3D_2E2 ) ) @ p )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(4,axiom,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combin_i_2E0 @ ( TA @ ( TA @ app_2E2 ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ei__thm) ).
thf(55,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combin_i_2E0 @ ( TA @ ( TA @ app_2E2 ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(56,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combin_i_2E0 @ ( TA @ ( TA @ app_2E2 ) ) ) )
= A ),
inference(cnf,[status(esa)],[55]) ).
thf(57,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combin_i_2E0 @ ( TA @ ( TA @ app_2E2 ) ) ) )
= A ),
inference(lifteq,[status(thm)],[56]) ).
thf(43,axiom,
! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
= ( B @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2Eword__sub__def) ).
thf(261,plain,
! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
= ( B @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(33,axiom,
! [TA: $tType,A: tyop_2Enum_2Enum] :
( ( A @ ( TA @ c_2Ewords_2En2w_2E1 ) )
= ( A @ ( TA @ c_2Ewords_2En2w_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( tyop_2Enum_2Enum @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27b) ).
thf(216,plain,
! [TA: $tType,A: tyop_2Enum_2Enum] :
( ( A @ ( TA @ c_2Ewords_2En2w_2E1 ) )
= ( A @ ( TA @ c_2Ewords_2En2w_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( tyop_2Enum_2Enum @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(40,axiom,
c_2Ebool_2ET_2E0 @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Etruth) ).
thf(253,plain,
c_2Ebool_2ET_2E0 @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ ( TB @ tyop_2Emin_2Efun ) @ ( TC @ tyop_2Emin_2Efun ),B: TB @ ( TC @ tyop_2Emin_2Efun ),C: TC] :
( ( C @ ( B @ ( A @ ( TA @ ( TB @ ( TC @ combin_s_2E0 ) ) @ ( TA @ ( TC @ tyop_2Emin_2Efun ) @ ( TB @ ( TC @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) @ ( TA @ ( TB @ tyop_2Emin_2Efun ) @ ( TC @ tyop_2Emin_2Efun ) @ app_2E2 ) ) ) @ ( TA @ ( TC @ tyop_2Emin_2Efun ) @ ( TB @ ( TC @ tyop_2Emin_2Efun ) @ app_2E2 ) ) ) @ ( TA @ ( TC @ app_2E2 ) ) ) )
= ( C @ ( B @ ( TB @ ( TC @ app_2E2 ) ) ) @ ( C @ ( A @ ( TA @ ( TB @ tyop_2Emin_2Efun ) @ ( TC @ app_2E2 ) ) ) @ ( TA @ ( TB @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Es__thm) ).
thf(61,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ ( TB @ tyop_2Emin_2Efun ) @ ( TC @ tyop_2Emin_2Efun ),B: TB @ ( TC @ tyop_2Emin_2Efun ),C: TC] :
( ( C @ ( B @ ( A @ ( TA @ ( TB @ ( TC @ combin_s_2E0 ) ) @ ( TA @ ( TC @ tyop_2Emin_2Efun ) @ ( TB @ ( TC @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) @ ( TA @ ( TB @ tyop_2Emin_2Efun ) @ ( TC @ tyop_2Emin_2Efun ) @ app_2E2 ) ) ) @ ( TA @ ( TC @ tyop_2Emin_2Efun ) @ ( TB @ ( TC @ tyop_2Emin_2Efun ) @ app_2E2 ) ) ) @ ( TA @ ( TC @ app_2E2 ) ) ) )
= ( C @ ( B @ ( TB @ ( TC @ app_2E2 ) ) ) @ ( C @ ( A @ ( TA @ ( TB @ tyop_2Emin_2Efun ) @ ( TC @ app_2E2 ) ) ) @ ( TA @ ( TB @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(366,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ( c_2Ebool_2ET_2E0 @ p )
!= ( A @ p ) )
| ~ $true
| ~ ( A @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ),
inference(paramod_ordered,[status(thm)],[175,122]) ).
thf(367,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ( c_2Ebool_2ET_2E0 @ p )
!= ( A @ p ) )
| ~ ( A @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ),
inference(simp,[status(thm)],[366]) ).
thf(368,plain,
~ ( c_2Ebool_2ET_2E0 @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ),
inference(pattern_uni,[status(thm)],[367:[bind(A,$thf( c_2Ebool_2ET_2E0 ))]]) ).
thf(392,plain,
( ( ( c_2Ebool_2ET_2E0 @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p )
!= ( c_2Ebool_2ET_2E0 @ p ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[175,368]) ).
thf(393,plain,
( ( c_2Ebool_2ET_2E0 @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p )
!= ( c_2Ebool_2ET_2E0 @ p ) ),
inference(simp,[status(thm)],[392]) ).
thf(396,plain,
( ( c_2Ebool_2ET_2E0 @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) )
!= c_2Ebool_2ET_2E0 ),
inference(simp,[status(thm)],[393]) ).
thf(14,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B @ ( A @ c_2Earithmetic_2E_2B_2E2 ) )
= ( B @ ( A @ ( c_2Earithmetic_2E_2B_2E0 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ app_2E2 ) ) ) @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Earithmetic_2E_2B_2E2) ).
thf(89,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B @ ( A @ c_2Earithmetic_2E_2B_2E2 ) )
= ( B @ ( A @ ( c_2Earithmetic_2E_2B_2E0 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ app_2E2 ) ) ) @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(111,plain,
! [TA: $tType,B: TA,A: TA] :
( ( ( B @ ( A @ ( TA @ c_2Emin_2E_3D_2E2 ) ) @ p )
| ( A != B ) )
& ( ( A = B )
| ~ ( B @ ( A @ ( TA @ c_2Emin_2E_3D_2E2 ) ) @ p ) ) ),
inference(cnf,[status(esa)],[110]) ).
thf(113,plain,
! [TA: $tType,B: TA,A: TA] :
( ( B @ ( A @ ( TA @ c_2Emin_2E_3D_2E2 ) ) @ p )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[111]) ).
thf(115,plain,
! [TA: $tType,B: TA,A: TA] :
( ( B @ ( A @ ( TA @ c_2Emin_2E_3D_2E2 ) ) @ p )
| ( A != B ) ),
inference(lifteq,[status(thm)],[113]) ).
thf(116,plain,
! [TA: $tType,A: TA] : ( A @ ( A @ ( TA @ c_2Emin_2E_3D_2E2 ) ) @ p ),
inference(simp,[status(thm)],[115]) ).
thf(9,axiom,
! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
= ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ewords_2Eword__add_2E2_2Emono_2EA_27a) ).
thf(74,plain,
! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
= ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,axiom,
! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
= ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27b) ).
thf(58,plain,
! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
= ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(59,plain,
! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
= ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) ) ),
inference(cnf,[status(esa)],[58]) ).
thf(60,plain,
! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
= ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) ) ),
inference(lifteq,[status(thm)],[59]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ tyop_2Emin_2Efun ),B: TA @ ( TB @ tyop_2Emin_2Efun )] :
( ! [C: TB] :
( ( C @ ( A @ ( TA @ ( TB @ app_2E2 ) ) ) )
= ( C @ ( B @ ( TA @ ( TB @ app_2E2 ) ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Eeq__ext) ).
thf(92,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ tyop_2Emin_2Efun ),B: TA @ ( TB @ tyop_2Emin_2Efun )] :
( ! [C: TB] :
( ( C @ ( A @ ( TA @ ( TB @ app_2E2 ) ) ) )
= ( C @ ( B @ ( TA @ ( TB @ app_2E2 ) ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(31,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( A @ p )
=> ( B @ p ) )
<=> ( B @ ( A @ ( c_2Emin_2E_3D_3D_3E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) ).
thf(197,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( B @ ( A @ ( c_2Emin_2E_3D_3D_3E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p )
=> ( ( A @ p )
=> ( B @ p ) ) )
& ( ( ( A @ p )
=> ( B @ p ) )
=> ( B @ ( A @ ( c_2Emin_2E_3D_3D_3E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(7,axiom,
! [A: tyop_2Emin_2Ebool] :
( ( A = c_2Ebool_2EF_2E0 )
| ( A = c_2Ebool_2ET_2E0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ebool__cases__ax) ).
thf(64,plain,
! [A: tyop_2Emin_2Ebool] :
( ( A = c_2Ebool_2EF_2E0 )
| ( A = c_2Ebool_2ET_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(65,plain,
! [A: tyop_2Emin_2Ebool] :
( ( A = c_2Ebool_2EF_2E0 )
| ( A = c_2Ebool_2ET_2E0 ) ),
inference(cnf,[status(esa)],[64]) ).
thf(66,plain,
! [A: tyop_2Emin_2Ebool] :
( ( A = c_2Ebool_2EF_2E0 )
| ( A = c_2Ebool_2ET_2E0 ) ),
inference(lifteq,[status(thm)],[65]) ).
thf(513,plain,
! [A: tyop_2Emin_2Ebool] :
( ( A
!= ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) ) )
| ( c_2Ebool_2ET_2E0 != c_2Ebool_2ET_2E0 )
| ( A = c_2Ebool_2EF_2E0 ) ),
inference(paramod_ordered,[status(thm)],[66,384]) ).
thf(514,plain,
! [A: tyop_2Emin_2Ebool] :
( ( A
!= ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) ) )
| ( A = c_2Ebool_2EF_2E0 ) ),
inference(simp,[status(thm)],[513]) ).
thf(515,plain,
( ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) )
= c_2Ebool_2EF_2E0 ),
inference(pattern_uni,[status(thm)],[514:[bind(A,$thf( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) ))]]) ).
thf(398,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ( A @ ( tyop_2Emin_2Ebool @ combin_i_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) )
!= ( c_2Ebool_2ET_2E0 @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) ) )
| ( A != c_2Ebool_2ET_2E0 ) ),
inference(paramod_ordered,[status(thm)],[57,396]) ).
thf(399,plain,
( ( c_2Ebool_2ET_2E0 @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ combin_i_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) ) ),
inference(simp,[status(thm)],[398]) ).
thf(454,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ( A @ ( tyop_2Emin_2Ebool @ combin_i_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) )
!= ( c_2Ebool_2ET_2E0 @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) ) )
| ( A
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ combin_i_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[57,399]) ).
thf(457,plain,
( ( c_2Ebool_2ET_2E0 @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ combin_i_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ combin_i_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) ) ),
inference(simp,[status(thm)],[454]) ).
thf(44,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A = B )
<=> ( B @ ( A @ ( TA @ c_2Emin_2E_3D_2E0 @ ( tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun ) @ ( TA @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( TA @ app_2E2 ) ) ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) ).
thf(264,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( B @ ( A @ ( TA @ c_2Emin_2E_3D_2E0 @ ( tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun ) @ ( TA @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( TA @ app_2E2 ) ) ) @ p )
=> ( A = B ) )
& ( ( A = B )
=> ( B @ ( A @ ( TA @ c_2Emin_2E_3D_2E0 @ ( tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun ) @ ( TA @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( TA @ app_2E2 ) ) ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(26,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( A @ p )
<=> ( B @ p ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Eboolext) ).
thf(149,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( B @ p )
=> ( A @ p ) )
& ( ( A @ p )
=> ( B @ p ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(30,axiom,
! [A: tyop_2Emin_2Ebool] :
( ( A @ c_2Ebool_2E_7E_2E1 @ p )
<=> ~ ( A @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_7E) ).
thf(191,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ~ ( A @ p )
=> ( A @ c_2Ebool_2E_7E_2E1 @ p ) )
& ( ( A @ c_2Ebool_2E_7E_2E1 @ p )
=> ~ ( A @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(32,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( A @ p )
=> ( ( B @ p )
=> ( C @ p ) ) )
<=> ( ( ( B @ p )
& ( A @ p ) )
=> ( C @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EAND__IMP__INTRO) ).
thf(204,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( ( B @ p )
& ( A @ p ) )
=> ( C @ p ) )
=> ( ( A @ p )
=> ( ( B @ p )
=> ( C @ p ) ) ) )
& ( ( ( A @ p )
=> ( ( B @ p )
=> ( C @ p ) ) )
=> ( ( ( B @ p )
& ( A @ p ) )
=> ( C @ p ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(68,plain,
! [TA: $tType,D: TA,C: TA,B: TA,A: TA] :
( ( ( D @ ( C @ ( c_2Ebool_2EF_2E0 @ ( TA @ c_2Ebool_2ECOND_2E3 ) ) ) )
= D )
& ( ( B @ ( A @ ( c_2Ebool_2ET_2E0 @ ( TA @ c_2Ebool_2ECOND_2E3 ) ) ) )
= A ) ),
inference(cnf,[status(esa)],[67]) ).
thf(69,plain,
! [TA: $tType,B: TA,A: TA] :
( ( B @ ( A @ ( c_2Ebool_2ET_2E0 @ ( TA @ c_2Ebool_2ECOND_2E3 ) ) ) )
= A ),
inference(cnfConj,[status(thm)],[68]) ).
thf(71,plain,
! [TA: $tType,B: TA,A: TA] :
( ( B @ ( A @ ( c_2Ebool_2ET_2E0 @ ( TA @ c_2Ebool_2ECOND_2E3 ) ) ) )
= A ),
inference(lifteq,[status(thm)],[69]) ).
thf(53,plain,
! [TA: $tType,B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
= ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) ) ),
inference(cnf,[status(esa)],[52]) ).
thf(54,plain,
! [TA: $tType,B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
= ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) ) ),
inference(lifteq,[status(thm)],[53]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( B @ ( A @ ( TA @ ( TB @ combin_k_2E0 ) @ ( TB @ ( TA @ tyop_2Emin_2Efun ) @ ( TB @ app_2E2 ) ) ) @ ( TB @ ( TA @ app_2E2 ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ek__thm) ).
thf(86,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( B @ ( A @ ( TA @ ( TB @ combin_k_2E0 ) @ ( TB @ ( TA @ tyop_2Emin_2Efun ) @ ( TB @ app_2E2 ) ) ) @ ( TB @ ( TA @ app_2E2 ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(29,axiom,
! [TA: $tType,A: tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun )] :
( ( A @ ( TA @ c_2Ebool_2E_3F_2E1 ) @ p )
<=> ? [B: TA] : ( B @ ( A @ ( tyop_2Emin_2Ebool @ ( TA @ app_2E2 ) ) ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantdef_2E_3F) ).
thf(187,plain,
! [TA: $tType,A: tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun )] :
( ( ? [B: TA] : ( B @ ( A @ ( tyop_2Emin_2Ebool @ ( TA @ app_2E2 ) ) ) @ p )
=> ( A @ ( TA @ c_2Ebool_2E_3F_2E1 ) @ p ) )
& ( ( A @ ( TA @ c_2Ebool_2E_3F_2E1 ) @ p )
=> ? [B: TA] : ( B @ ( A @ ( tyop_2Emin_2Ebool @ ( TA @ app_2E2 ) ) ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType] :
( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( A @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
= ( A @ ( B @ c_2Earithmetic_2E_2D_2E2 ) @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( B @ ( A @ c_2Earithmetic_2E_2D_2E2 ) @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( A @ ( B @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ c_2Ebool_2ECOND_2E3 ) ) ) ) )
& ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B @ ( TB @ c_2Ewords_2En2w_2E1 ) @ ( TB @ c_2Ewords_2Eword__2comp_2E1 ) @ ( A @ ( TB @ c_2Ewords_2En2w_2E1 ) @ ( TB @ c_2Ewords_2Eword__2comp_2E1 ) @ ( TB @ c_2Ewords_2Eword__add_2E2 ) ) )
= ( B @ ( A @ c_2Earithmetic_2E_2B_2E2 ) @ ( TB @ c_2Ewords_2En2w_2E1 ) @ ( TB @ c_2Ewords_2Eword__2comp_2E1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LITERAL__ADD) ).
thf(219,plain,
! [TA: $tType,TB: $tType] :
( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( A @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
= ( A @ ( B @ c_2Earithmetic_2E_2D_2E2 ) @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( B @ ( A @ c_2Earithmetic_2E_2D_2E2 ) @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( A @ ( B @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ c_2Ebool_2ECOND_2E3 ) ) ) ) )
& ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B @ ( TB @ c_2Ewords_2En2w_2E1 ) @ ( TB @ c_2Ewords_2Eword__2comp_2E1 ) @ ( A @ ( TB @ c_2Ewords_2En2w_2E1 ) @ ( TB @ c_2Ewords_2Eword__2comp_2E1 ) @ ( TB @ c_2Ewords_2Eword__add_2E2 ) ) )
= ( B @ ( A @ c_2Earithmetic_2E_2B_2E2 ) @ ( TB @ c_2Ewords_2En2w_2E1 ) @ ( TB @ c_2Ewords_2Eword__2comp_2E1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(316,plain,
( ( ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ p )
!= ( c_2Ebool_2EF_2E0 @ p ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,102]) ).
thf(317,plain,
( ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ p )
!= ( c_2Ebool_2EF_2E0 @ p ) ),
inference(simp,[status(thm)],[316]) ).
thf(318,plain,
( ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) )
!= c_2Ebool_2EF_2E0 ),
inference(simp,[status(thm)],[317]) ).
thf(17,axiom,
! [TA: $tType,A: tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun )] :
( ( A @ ( TA @ c_2Ebool_2E_3F_2E1 ) )
= ( A @ ( TA @ c_2Ebool_2E_3F_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun ) @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) ).
thf(98,plain,
! [TA: $tType,A: tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun )] :
( ( A @ ( TA @ c_2Ebool_2E_3F_2E1 ) )
= ( A @ ( TA @ c_2Ebool_2E_3F_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun ) @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(45,axiom,
! [A: tyop_2Emin_2Ebool] :
( ( ( ( A @ p )
=> ( c_2Ebool_2EF_2E0 @ p ) )
<=> ~ ( A @ p ) )
& ( ( ( A @ p )
=> ( A @ p ) )
<=> ( c_2Ebool_2ET_2E0 @ p ) )
& ( ( ( c_2Ebool_2EF_2E0 @ p )
=> ( A @ p ) )
<=> ( c_2Ebool_2ET_2E0 @ p ) )
& ( ( ( A @ p )
=> ( c_2Ebool_2ET_2E0 @ p ) )
<=> ( c_2Ebool_2ET_2E0 @ p ) )
& ( ( ( c_2Ebool_2ET_2E0 @ p )
=> ( A @ p ) )
<=> ( A @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__CLAUSES) ).
thf(271,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ~ ( A @ p )
=> ( ( A @ p )
=> ( c_2Ebool_2EF_2E0 @ p ) ) )
& ( ( ( A @ p )
=> ( c_2Ebool_2EF_2E0 @ p ) )
=> ~ ( A @ p ) )
& ( c_2Ebool_2ET_2E0 @ p )
& ( ( c_2Ebool_2ET_2E0 @ p )
=> ( ( c_2Ebool_2EF_2E0 @ p )
=> ( A @ p ) ) )
& ( ( ( c_2Ebool_2EF_2E0 @ p )
=> ( A @ p ) )
=> ( c_2Ebool_2ET_2E0 @ p ) )
& ( ( c_2Ebool_2ET_2E0 @ p )
=> ( ( A @ p )
=> ( c_2Ebool_2ET_2E0 @ p ) ) )
& ( ( ( A @ p )
=> ( c_2Ebool_2ET_2E0 @ p ) )
=> ( c_2Ebool_2ET_2E0 @ p ) )
& ( ( A @ p )
=> ( ( c_2Ebool_2ET_2E0 @ p )
=> ( A @ p ) ) )
& ( ( ( c_2Ebool_2ET_2E0 @ p )
=> ( A @ p ) )
=> ( A @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(386,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ( A @ ( tyop_2Emin_2Ebool @ combin_i_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) )
!= ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) ) )
| ( A != c_2Ebool_2ET_2E0 ) ),
inference(paramod_ordered,[status(thm)],[57,384]) ).
thf(387,plain,
( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ combin_i_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) )
!= ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) ) ),
inference(simp,[status(thm)],[386]) ).
thf(19,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( B @ p )
| ( A @ p ) )
<=> ( B @ ( A @ ( c_2Ebool_2E_5C_2F_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) ).
thf(103,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( B @ ( A @ ( c_2Ebool_2E_5C_2F_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p )
=> ( ( B @ p )
| ( A @ p ) ) )
& ( ( ( B @ p )
| ( A @ p ) )
=> ( B @ ( A @ ( c_2Ebool_2E_5C_2F_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(35,axiom,
c_2Ebool_2ET_2E0 @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
thf(226,plain,
c_2Ebool_2ET_2E0 @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(11,axiom,
! [TA: $tType,A: tyop_2Emin_2Ebool,B: TA,C: TA] :
( ( C @ ( B @ ( A @ ( TA @ c_2Ebool_2ECOND_2E3 ) ) ) )
= ( C @ ( B @ ( A @ ( TA @ c_2Ebool_2ECOND_2E0 @ ( TA @ ( TA @ tyop_2Emin_2Efun ) @ ( TA @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( TA @ ( TA @ tyop_2Emin_2Efun ) @ ( TA @ app_2E2 ) ) ) @ ( TA @ ( TA @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a) ).
thf(80,plain,
! [TA: $tType,A: tyop_2Emin_2Ebool,B: TA,C: TA] :
( ( C @ ( B @ ( A @ ( TA @ c_2Ebool_2ECOND_2E3 ) ) ) )
= ( C @ ( B @ ( A @ ( TA @ c_2Ebool_2ECOND_2E0 @ ( TA @ ( TA @ tyop_2Emin_2Efun ) @ ( TA @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( TA @ ( TA @ tyop_2Emin_2Efun ) @ ( TA @ app_2E2 ) ) ) @ ( TA @ ( TA @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(22,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B @ ( A @ c_2Earithmetic_2E_2D_2E2 ) )
= ( B @ ( A @ ( c_2Earithmetic_2E_2D_2E0 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ app_2E2 ) ) ) @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Earithmetic_2E_2D_2E2) ).
thf(123,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B @ ( A @ c_2Earithmetic_2E_2D_2E2 ) )
= ( B @ ( A @ ( c_2Earithmetic_2E_2D_2E0 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ app_2E2 ) ) ) @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(192,plain,
( ! [A: tyop_2Emin_2Ebool] :
( ~ ( A @ p )
=> ( A @ c_2Ebool_2E_7E_2E1 @ p ) )
& ! [A: tyop_2Emin_2Ebool] :
( ( A @ c_2Ebool_2E_7E_2E1 @ p )
=> ~ ( A @ p ) ) ),
inference(miniscope,[status(thm)],[191]) ).
thf(193,plain,
! [B: tyop_2Emin_2Ebool,A: tyop_2Emin_2Ebool] :
( ( ( B @ c_2Ebool_2E_7E_2E1 @ p )
| ( B @ p ) )
& ( ~ ( A @ p )
| ~ ( A @ c_2Ebool_2E_7E_2E1 @ p ) ) ),
inference(cnf,[status(esa)],[192]) ).
thf(194,plain,
! [A: tyop_2Emin_2Ebool] :
( ~ ( A @ p )
| ~ ( A @ c_2Ebool_2E_7E_2E1 @ p ) ),
inference(cnfConj,[status(thm)],[193]) ).
thf(62,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: TA,B: TB @ ( TA @ tyop_2Emin_2Efun ),A: TC @ ( TB @ tyop_2Emin_2Efun ) @ ( TA @ tyop_2Emin_2Efun )] :
( ( C @ ( B @ ( A @ ( TC @ ( TB @ ( TA @ combin_s_2E0 ) ) @ ( TC @ ( TA @ tyop_2Emin_2Efun ) @ ( TB @ ( TA @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) @ ( TC @ ( TB @ tyop_2Emin_2Efun ) @ ( TA @ tyop_2Emin_2Efun ) @ app_2E2 ) ) ) @ ( TC @ ( TA @ tyop_2Emin_2Efun ) @ ( TB @ ( TA @ tyop_2Emin_2Efun ) @ app_2E2 ) ) ) @ ( TC @ ( TA @ app_2E2 ) ) ) )
= ( C @ ( B @ ( TB @ ( TA @ app_2E2 ) ) ) @ ( C @ ( A @ ( TC @ ( TB @ tyop_2Emin_2Efun ) @ ( TA @ app_2E2 ) ) ) @ ( TC @ ( TB @ app_2E2 ) ) ) ) ),
inference(cnf,[status(esa)],[61]) ).
thf(63,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: TA,B: TB @ ( TA @ tyop_2Emin_2Efun ),A: TC @ ( TB @ tyop_2Emin_2Efun ) @ ( TA @ tyop_2Emin_2Efun )] :
( ( C @ ( B @ ( A @ ( TC @ ( TB @ ( TA @ combin_s_2E0 ) ) @ ( TC @ ( TA @ tyop_2Emin_2Efun ) @ ( TB @ ( TA @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) @ ( TC @ ( TB @ tyop_2Emin_2Efun ) @ ( TA @ tyop_2Emin_2Efun ) @ app_2E2 ) ) ) @ ( TC @ ( TA @ tyop_2Emin_2Efun ) @ ( TB @ ( TA @ tyop_2Emin_2Efun ) @ app_2E2 ) ) ) @ ( TC @ ( TA @ app_2E2 ) ) ) )
= ( C @ ( B @ ( TB @ ( TA @ app_2E2 ) ) ) @ ( C @ ( A @ ( TC @ ( TB @ tyop_2Emin_2Efun ) @ ( TA @ app_2E2 ) ) ) @ ( TC @ ( TB @ app_2E2 ) ) ) ) ),
inference(lifteq,[status(thm)],[62]) ).
thf(46,axiom,
! [TA: $tType,A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: TA,D: TA,E: TA,F: TA] :
( ( ( ~ ( B @ p )
=> ( E = F ) )
& ( ( B @ p )
=> ( C = D ) )
& ( A = B ) )
=> ( ( E @ ( C @ ( A @ ( TA @ c_2Ebool_2ECOND_2E3 ) ) ) )
= ( F @ ( D @ ( B @ ( TA @ c_2Ebool_2ECOND_2E3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CONG) ).
thf(295,plain,
! [TA: $tType,A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: TA,D: TA,E: TA,F: TA] :
( ( ( ~ ( B @ p )
=> ( E = F ) )
& ( ( B @ p )
=> ( C = D ) )
& ( A = B ) )
=> ( ( E @ ( C @ ( A @ ( TA @ c_2Ebool_2ECOND_2E3 ) ) ) )
= ( F @ ( D @ ( B @ ( TA @ c_2Ebool_2ECOND_2E3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(16,axiom,
! [TA: $tType,A: tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun )] :
( ( A @ ( TA @ c_2Ebool_2E_21_2E1 ) )
= ( A @ ( TA @ c_2Ebool_2E_21_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun ) @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) ).
thf(95,plain,
! [TA: $tType,A: tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun )] :
( ( A @ ( TA @ c_2Ebool_2E_21_2E1 ) )
= ( A @ ( TA @ c_2Ebool_2E_21_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun ) @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(328,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ( A @ c_2Ebool_2E_7E_2E1 @ p )
!= ( c_2Ebool_2ET_2E0 @ p ) )
| ~ ( A @ p )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[175,194]) ).
thf(329,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ( A @ c_2Ebool_2E_7E_2E1 @ p )
!= ( c_2Ebool_2ET_2E0 @ p ) )
| ~ ( A @ p ) ),
inference(simp,[status(thm)],[328]) ).
thf(336,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ( A @ c_2Ebool_2E_7E_2E1 )
!= c_2Ebool_2ET_2E0 )
| ~ ( A @ p ) ),
inference(simp,[status(thm)],[329]) ).
thf(39,axiom,
! [TA: $tType,A: tyop_2Enum_2Enum] :
( ( A @ ( TA @ c_2Ewords_2En2w_2E1 ) )
= ( A @ ( TA @ c_2Ewords_2En2w_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( tyop_2Enum_2Enum @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27a) ).
thf(250,plain,
! [TA: $tType,A: tyop_2Enum_2Enum] :
( ( A @ ( TA @ c_2Ewords_2En2w_2E1 ) )
= ( A @ ( TA @ c_2Ewords_2En2w_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( tyop_2Enum_2Enum @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(325,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ p )
!= ( A @ p ) )
| ~ $true
| ~ ( A @ c_2Ebool_2E_7E_2E1 @ p ) ),
inference(paramod_ordered,[status(thm)],[49,194]) ).
thf(326,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ p )
!= ( A @ p ) )
| ~ ( A @ c_2Ebool_2E_7E_2E1 @ p ) ),
inference(simp,[status(thm)],[325]) ).
thf(327,plain,
~ ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ c_2Ebool_2E_7E_2E1 @ p ),
inference(pattern_uni,[status(thm)],[326:[bind(A,$thf( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) ))]]) ).
thf(342,plain,
( ( ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ c_2Ebool_2E_7E_2E1 @ p )
!= ( c_2Ebool_2ET_2E0 @ p ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[175,327]) ).
thf(343,plain,
( ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ c_2Ebool_2E_7E_2E1 @ p )
!= ( c_2Ebool_2ET_2E0 @ p ) ),
inference(simp,[status(thm)],[342]) ).
thf(345,plain,
( ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ c_2Ebool_2E_7E_2E1 )
!= c_2Ebool_2ET_2E0 ),
inference(simp,[status(thm)],[343]) ).
thf(579,plain,
! [A: tyop_2Emin_2Ebool] :
( ( A
!= ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ c_2Ebool_2E_7E_2E1 ) )
| ( c_2Ebool_2ET_2E0 != c_2Ebool_2ET_2E0 )
| ( A = c_2Ebool_2EF_2E0 ) ),
inference(paramod_ordered,[status(thm)],[66,345]) ).
thf(580,plain,
! [A: tyop_2Emin_2Ebool] :
( ( A
!= ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ c_2Ebool_2E_7E_2E1 ) )
| ( A = c_2Ebool_2EF_2E0 ) ),
inference(simp,[status(thm)],[579]) ).
thf(581,plain,
( ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ c_2Ebool_2E_7E_2E1 )
= c_2Ebool_2EF_2E0 ),
inference(pattern_uni,[status(thm)],[580:[bind(A,$thf( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ c_2Ebool_2E_7E_2E1 ))]]) ).
thf(42,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B @ ( A @ c_2Earithmetic_2E_3C_3D_2E2 ) )
= ( B @ ( A @ ( c_2Earithmetic_2E_3C_3D_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2) ).
thf(258,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B @ ( A @ c_2Earithmetic_2E_3C_3D_2E2 ) )
= ( B @ ( A @ ( c_2Earithmetic_2E_3C_3D_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(28,axiom,
! [TA: $tType,A: TA] :
( ( A = A )
<=> ( c_2Ebool_2ET_2E0 @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EREFL__CLAUSE) ).
thf(186,plain,
c_2Ebool_2ET_2E0 @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(400,plain,
( ( c_2Ebool_2ET_2E0 != c_2Ebool_2ET_2E0 )
| ( c_2Ebool_2E_7E_2E0
!= ( tyop_2Emin_2Ebool @ combin_i_2E0 ) ) ),
inference(simp,[status(thm)],[398]) ).
thf(401,plain,
( c_2Ebool_2E_7E_2E0
!= ( tyop_2Emin_2Ebool @ combin_i_2E0 ) ),
inference(simp,[status(thm)],[400]) ).
thf(37,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( B @ ( A @ c_2Ebool_2E_2F_5C_2E2 ) @ p )
<=> ( ( B @ p )
& ( A @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_2F_5C) ).
thf(235,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( B @ p )
& ( A @ p ) )
=> ( B @ ( A @ c_2Ebool_2E_2F_5C_2E2 ) @ p ) )
& ( ( B @ ( A @ c_2Ebool_2E_2F_5C_2E2 ) @ p )
=> ( ( B @ p )
& ( A @ p ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(378,plain,
( ( ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p )
!= ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ p ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,363]) ).
thf(379,plain,
( ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p )
!= ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ p ) ),
inference(simp,[status(thm)],[378]) ).
thf(383,plain,
( ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) )
!= ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) ) ),
inference(simp,[status(thm)],[379]) ).
thf(25,axiom,
! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
= ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ewords_2Eword__sub_2E2_2Emono_2EA_27a) ).
thf(146,plain,
! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
= ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(50,plain,
( ( sk2 @ ( sk1 @ c_2Earithmetic_2E_2D_2E2 ) @ ( skt1 @ c_2Ewords_2En2w_2E1 ) )
!= ( sk2 @ ( skt1 @ c_2Ewords_2En2w_2E1 ) @ ( sk1 @ ( skt1 @ c_2Ewords_2En2w_2E1 ) @ ( skt1 @ c_2Ewords_2Eword__sub_2E2 ) ) ) ),
inference(cnfConj,[status(thm)],[48]) ).
thf(51,plain,
( ( sk2 @ ( sk1 @ c_2Earithmetic_2E_2D_2E2 ) @ ( skt1 @ c_2Ewords_2En2w_2E1 ) )
!= ( sk2 @ ( skt1 @ c_2Ewords_2En2w_2E1 ) @ ( sk1 @ ( skt1 @ c_2Ewords_2En2w_2E1 ) @ ( skt1 @ c_2Ewords_2Eword__sub_2E2 ) ) ) ),
inference(lifteq,[status(thm)],[50]) ).
thf(330,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ( c_2Ebool_2ET_2E0 @ p )
!= ( A @ p ) )
| ~ $true
| ~ ( A @ c_2Ebool_2E_7E_2E1 @ p ) ),
inference(paramod_ordered,[status(thm)],[175,194]) ).
thf(331,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ( c_2Ebool_2ET_2E0 @ p )
!= ( A @ p ) )
| ~ ( A @ c_2Ebool_2E_7E_2E1 @ p ) ),
inference(simp,[status(thm)],[330]) ).
thf(332,plain,
~ ( c_2Ebool_2ET_2E0 @ c_2Ebool_2E_7E_2E1 @ p ),
inference(pattern_uni,[status(thm)],[331:[bind(A,$thf( c_2Ebool_2ET_2E0 ))]]) ).
thf(346,plain,
( ( ( c_2Ebool_2ET_2E0 @ c_2Ebool_2E_7E_2E1 @ p )
!= ( c_2Ebool_2ET_2E0 @ p ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[175,332]) ).
thf(347,plain,
( ( c_2Ebool_2ET_2E0 @ c_2Ebool_2E_7E_2E1 @ p )
!= ( c_2Ebool_2ET_2E0 @ p ) ),
inference(simp,[status(thm)],[346]) ).
thf(350,plain,
( ( c_2Ebool_2ET_2E0 @ c_2Ebool_2E_7E_2E1 )
!= c_2Ebool_2ET_2E0 ),
inference(simp,[status(thm)],[347]) ).
thf(562,plain,
! [A: tyop_2Emin_2Ebool] :
( ( A
!= ( c_2Ebool_2ET_2E0 @ c_2Ebool_2E_7E_2E1 ) )
| ( c_2Ebool_2ET_2E0 != c_2Ebool_2ET_2E0 )
| ( A = c_2Ebool_2EF_2E0 ) ),
inference(paramod_ordered,[status(thm)],[66,350]) ).
thf(563,plain,
! [A: tyop_2Emin_2Ebool] :
( ( A
!= ( c_2Ebool_2ET_2E0 @ c_2Ebool_2E_7E_2E1 ) )
| ( A = c_2Ebool_2EF_2E0 ) ),
inference(simp,[status(thm)],[562]) ).
thf(564,plain,
( ( c_2Ebool_2ET_2E0 @ c_2Ebool_2E_7E_2E1 )
= c_2Ebool_2EF_2E0 ),
inference(pattern_uni,[status(thm)],[563:[bind(A,$thf( c_2Ebool_2ET_2E0 @ c_2Ebool_2E_7E_2E1 ))]]) ).
thf(38,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( B @ ( A @ c_2Ebool_2E_5C_2F_2E2 ) @ p )
<=> ( ( B @ p )
| ( A @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_5C_2F) ).
thf(242,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( B @ p )
| ( A @ p ) )
=> ( B @ ( A @ c_2Ebool_2E_5C_2F_2E2 ) @ p ) )
& ( ( B @ ( A @ c_2Ebool_2E_5C_2F_2E2 ) @ p )
=> ( ( B @ p )
| ( A @ p ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(23,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ( B @ p )
=> ( C = D ) )
& ( A = B ) )
=> ( ( ( A @ p )
=> ( C @ p ) )
<=> ( ( B @ p )
=> ( D @ p ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__CONG) ).
thf(126,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ( B @ p )
=> ( C = D ) )
& ( A = B ) )
=> ( ( ( ( B @ p )
=> ( D @ p ) )
=> ( ( A @ p )
=> ( C @ p ) ) )
& ( ( ( A @ p )
=> ( C @ p ) )
=> ( ( B @ p )
=> ( D @ p ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(390,plain,
( ( ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ p )
!= ( c_2Ebool_2ET_2E0 @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,368]) ).
thf(391,plain,
( ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) @ p )
!= ( c_2Ebool_2ET_2E0 @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ),
inference(simp,[status(thm)],[390]) ).
thf(395,plain,
( ( sk1 @ ( sk2 @ c_2Earithmetic_2E_3C_3D_2E2 ) )
!= ( c_2Ebool_2ET_2E0 @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) ) ),
inference(simp,[status(thm)],[391]) ).
thf(12,axiom,
! [TA: $tType,A: tyop_2Emin_2Ebool,B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( C @ ( B @ ( A @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ c_2Ebool_2ECOND_2E3 ) ) ) )
= ( C @ ( B @ ( A @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ c_2Ebool_2ECOND_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27b_29) ).
thf(83,plain,
! [TA: $tType,A: tyop_2Emin_2Ebool,B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( C @ ( B @ ( A @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ c_2Ebool_2ECOND_2E3 ) ) ) )
= ( C @ ( B @ ( A @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ c_2Ebool_2ECOND_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(41,axiom,
! [TA: $tType,A: tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun )] :
( ( A @ ( TA @ c_2Ebool_2E_21_2E1 ) @ p )
<=> ! [B: TA] : ( B @ ( A @ ( tyop_2Emin_2Ebool @ ( TA @ app_2E2 ) ) ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantdef_2E_21) ).
thf(254,plain,
! [TA: $tType,A: tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun )] :
( ( ! [B: TA] : ( B @ ( A @ ( tyop_2Emin_2Ebool @ ( TA @ app_2E2 ) ) ) @ p )
=> ( A @ ( TA @ c_2Ebool_2E_21_2E1 ) @ p ) )
& ( ( A @ ( TA @ c_2Ebool_2E_21_2E1 ) @ p )
=> ! [B: TA] : ( B @ ( A @ ( tyop_2Emin_2Ebool @ ( TA @ app_2E2 ) ) ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(36,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( B @ p )
& ( A @ p ) )
<=> ( B @ ( A @ ( c_2Ebool_2E_2F_5C_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) ).
thf(227,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( B @ ( A @ ( c_2Ebool_2E_2F_5C_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p )
=> ( ( B @ p )
& ( A @ p ) ) )
& ( ( ( B @ p )
& ( A @ p ) )
=> ( B @ ( A @ ( c_2Ebool_2E_2F_5C_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(907,plain,
$false,
inference(e,[status(thm)],[384,77,311,67,138,101,52,110,57,261,216,253,61,396,89,116,74,102,60,117,92,197,515,457,264,64,149,191,204,71,54,49,86,159,187,219,318,98,271,387,103,66,399,226,80,123,194,63,295,95,336,175,250,363,581,368,258,186,55,401,58,235,383,146,51,564,242,126,395,47,122,83,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP013_3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.17/0.59 % Computer : n026.cluster.edu
% 0.17/0.59 % Model : x86_64 x86_64
% 0.17/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.59 % Memory : 8046.5625MB
% 0.17/0.59 % OS : Linux 6.8.0-71-generic
% 0.17/0.59 % CPULimit : 300
% 0.17/0.59 % WCLimit : 300
% 0.17/0.59 % DateTime : Fri Sep 25 17:21:13 UTC 2026
% 0.17/0.59 % CPUTime :
% 0.17/0.59 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.95/1.18 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.52/1.44 % [INFO] Parsing done (266ms).
% 1.52/1.46 % [INFO] Running in sequential loop mode.
% 2.42/1.86 % [INFO] eprover registered as external prover.
% 2.42/1.87 % [INFO] Scanning for conjecture ...
% 2.65/2.02 % [INFO] Found a conjecture (or negated_conjecture) and 45 axioms. Running axiom selection ...
% 2.91/2.12 % [INFO] Axiom selection finished. Selected 44 axioms (removed 1 axioms).
% 3.37/2.25 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.37/2.27 % [INFO] Type checking passed.
% 3.37/2.27 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 4.10/2.57 % [INFO] [Domain constraints] Detected constraint on tyop_2Emin_2Ebool
% 4.10/2.57 % [INFO] [Domain constraints] dom(tyop_2Emin_2Ebool) ⊆ {c_2Ebool_2ET_2E0,c_2Ebool_2EF_2E0}
% 23.69/8.73 % External prover 'e' found a proof!
% 23.69/8.73 % [INFO] Killing All external provers ...
% 23.69/8.74 % Time passed: 7999ms (effective reasoning time: 7268ms)
% 23.69/8.74 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 23.69/8.74 % Axioms used in derivation (44): thm_2Eextra_2Dho_2Eeq__ext, thm_2Eextra_2Dho_2Eboolext, arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27b, logicdef_2E_5C_2F, thm_2Eextra_2Dho_2Ek__thm, arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27a, logicdef_2E_3D_3D_3E, arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a, thm_2Eextra_2Dho_2Etruth, arityeq2_2Ec_2Ewords_2Eword__add_2E2_2Emono_2EA_27b, arityeq2_2Ec_2Earithmetic_2E_2B_2E2, arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a, logicdef_2E_2F_5C, logicdef_2E_7E, quantdef_2E_3F, thm_2Ewords_2Eword__sub__def, thm_2Ebool_2EREFL__CLAUSE, arityeq2_2Ec_2Earithmetic_2E_2D_2E2, logicdef_2E_3D, thm_2Ebool_2EEQ__CLAUSES, arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2, thm_2Eextra_2Dho_2Ei__thm, thm_2Ebool_2EIMP__CONG, arityeq2_2Ec_2Ebool_2E_2F_5C_2E2, arityeq2_2Ec_2Ewords_2Eword__sub_2E2_2Emono_2EA_27a, thm_2Ewords_2EWORD__LITERAL__ADD, arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2, thm_2Eextra_2Dho_2Ebool__cases__ax, arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27b_29, thm_2Eextra_2Dho_2Enotfalse, thm_2Ebool_2ECOND__CONG, thm_2Ebool_2EAND__IMP__INTRO, arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27a, quantdef_2E_21, arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a, thm_2Ebool_2EIMP__CLAUSES, thm_2Ebool_2ETRUTH, arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27b, arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a, arityeq1_2Ec_2Ebool_2E_7E_2E1, arityeq2_2Ec_2Ebool_2E_5C_2F_2E2, thm_2Eextra_2Dho_2Es__thm, arityeq2_2Ec_2Ewords_2Eword__add_2E2_2Emono_2EA_27a, thm_2Ebool_2Ebool__case__thm
% 23.69/8.74 % No. of inferences in proof: 182
% 23.69/8.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7999 ms resp. 7268 ms w/o parsing
% 23.69/8.79 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 23.69/8.79 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------